A Straight Construction Algorithm for a Delay Invariant Convolutional Network Coding on Cyclic Networks

Delay invariant convolutional network codes (abbreviated DI-CNCs) can guarantee multicast communication at asymptotically optimal rates in networks with any delay profile. For a cyclic network, it has been shown that one can associate it with an acyclic network consisting of nodes in five layers, and the acyclic algorithm of
$\mathbb {F}$
-linear multicast can be employed to construct a DI-
$\mathbb {F}$
-CNC, as long as the field size is larger than the number of sinks in the cyclic network. In this paper, we present a directly feasible construction algorithm for a DI-
$\mathbb {F}$
-CNC over a cyclic network. Complexity of code construction and theoretical guarantees of algorithm implementation are also investigated in detail. The advantage of the straight construction algorithm is that for an existing code, when some sink nodes and associated edges are added, our algorithm just modifies the new assigned coding coefficients in an efficient localized manner, without the necessity to construct again the code in its expanding network.